{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# The NEST `noise_generator`\n",
    "\n",
    "#### Hans Ekkehard Plesser, 2015-06-25\n",
    "\n",
    "This notebook describes how the NEST `noise_generator` model works and what effect it has on model neurons.\n",
    "\n",
    "NEST needs to be in your `PYTHONPATH` to run this notebook.\n",
    "\n",
    "## Basics\n",
    "\n",
    "The `noise_generator` emits \n",
    "\n",
    "1. a piecewise constant current \n",
    "1. that changes at fixed intervals $\\delta$. \n",
    "1. For each interval, a new amplitude is chosen from the normal distribution.\n",
    "1. Each target neuron receives a different realization of the current.\n",
    "\n",
    "To be precise, the output current of the generator is given by\n",
    "\n",
    "$$I(t) = \\mu + \\sigma N_j \\qquad\\text{with $j$ such that}\\quad j\\delta < t \\leq (j+1)\\delta$$\n",
    "\n",
    "where $N_j$ is the value drawn from the zero-mean unit-variance normal distribution for interval $j$ containing $t$.  \n",
    "\n",
    "When using the generator with modulated variance, the noise current is given by\n",
    "\n",
    "$$I(t) = \\mu + \\sqrt{\\sigma^2 + \\sigma_m^2\\sin(2\\pi f j\\delta + \\frac{2\\pi}{360}\\phi_d)} N_j \\;.$$\n",
    "\n",
    "Mathematical symbols match model parameters as follows\n",
    "\n",
    "|Symbol|Parameter|Unit|Default|Description|\n",
    "|------|:--------|:---|------:|:----------|\n",
    "|$\\mu$|`mean`|pA|0 pA|mean of the noise current amplitude|\n",
    "|$\\sigma$|`std`|pA|0 pA|standard deviation of the noise current amplitude|\n",
    "|$\\sigma_m$|`std_mod`|pA|0 pA|modulation depth of the std. deviation of the noise current amplitude|\n",
    "|$\\delta$|`dt`|ms|1 ms|interval between current amplitude changes|\n",
    "|$f$|`frequency`|Hz|0 Hz| frequency of variance modulation|\n",
    "|$\\phi_d$|`phase`|[deg]|0$^{\\circ}$| phase of variance modulation|\n",
    "\n",
    "For the remainder of this document, we will only consider the current at time points $t_j=j\\delta$ and define\n",
    "\n",
    "$$I_j = I(t_j+) = \\mu + \\sigma N_j $$\n",
    "\n",
    "and correspondingly for the case of modulated noise. Note that $I_j$ is thus the current emitted during $(t_j, t_{j+1}]$, following NEST's use of left-open, right-closed intervals. We also set $\\omega=2\\pi f$ and $\\phi=\\frac{2\\pi}{360}\\phi_d$ for brevity.\n",
    "\n",
    "### Properties of the noise current\n",
    "\n",
    "1. The noise current is a *piecewise constant* current. Thus, it is only an approximation to white noise and the properties of the noise will depend on the update interval $\\delta$. The default update interval is $\\delta = 1$ms. We chose this value so that the default would be independent from the time step $h$ of the simulation, assuming that time steps larger than 1 ms are rarely used. It also is plausible to assume that most time steps chosen will divide 1 ms evenly, so that changes in current amplitude will coincide with time steps. If this is not the case, the subsequent analysis does not apply exactly.\n",
    "1. The currents to all targets of a noise generator have different amplitudes, but always change simultaneously at times $j\\delta$.\n",
    "1. Across an ensemble of targets or realizations, we have\n",
    "$$\\begin{align}\n",
    "\\langle I_j\\rangle &= \\mu \\\\\n",
    "\\langle \\Delta I_j^2\\rangle &= \\sigma^2 \\qquad \\text{without modulation} \\\\\n",
    "\\langle \\Delta I_j^2\\rangle &= \\sigma^2 + \\sigma_m^2\\sin( \\omega j\\delta + \\phi) \\qquad \\text{with modulation.} \n",
    "\\end{align}$$\n",
    "1. Without modulation, the autocorrelation of the noise is given by\n",
    "$$\\langle (I_j-\\mu) (I_k-\\mu)\\rangle = \\sigma^2\\delta_{jk}$$ \\\n",
    "where $\\delta_{jk}$ is Kronecker's delta.\n",
    "1. With modulation, the autocorrlation is\n",
    "$$\\langle (I_j-\\mu) (I_k-\\mu)\\rangle = \\sigma_j^2\\delta_{jk}\\qquad\\text{where}\\; \\sigma_j = \\sqrt{\\sigma^2 + \\sigma_m^2\\sin( j\\delta\\omega + \\phi_d)}\\;.$$ \\\n",
    "Note that it is currently not possible to record this noise current directly in NEST, since a `multimeter` cannot record from a `noise_generator`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Noise generators effect on a neuron\n",
    "\n",
    "Precisely how a current injected into a neuron will affect that neuron, will obviously depend on the neuron itself. We consider here the subthreshold dynamics most widely used in NEST, namely the leaky integrator. The analysis that follows is applicable directly to all `iaf_psc_*` models. It applies to conductance based neurons such as the `iaf_cond_*` models only as long as no synaptic input is present, which changes the membrane conductances.\n",
    "\n",
    "### Membrane potential dynamics\n",
    "\n",
    "We focus here only on subthreshold dynamics, i.e., we assume that the firing threshold of the neuron is $V_{\\text{th}}=\\infty$. We also ignore all synaptic input, which is valid for linear models, and set the resting potential $E_L=0$ mV for convenience. The membrane potential $V$ is then governed by\n",
    "\n",
    "$$\\dot{V} = - \\frac{V}{\\tau} + \\frac{I}{C}$$\n",
    "\n",
    "where $\\tau$ is the membrane time constant and $C$ the capacitance. We further assume $V(0)=0$ mV. We now focus on the membrane potential at times $t_j=j\\delta$. Let $V_j=V(j\\delta)$ be the membrane potential at time $t_j$. Then, a constant current $I_j$ will be applied to the neuron until $t_{j+1}=t_j+\\delta$, at which time the membrane potential will be\n",
    "\n",
    "$$V_{j+1} = V_j e^{-\\delta/\\tau} + \\left(1-e^{-\\delta/\\tau}\\right)\\frac{I_j\\tau}{C} \\;.$$\n",
    "\n",
    "We can apply this backward in time towards $V_0=0$\n",
    "\n",
    "$$\\begin{align}\n",
    "V_{j+1} &= V_j e^{-\\delta/\\tau} + \\left(1-e^{-\\delta/\\tau}\\right)\\frac{I_j\\tau}{C} \\\\\n",
    "  &= \\left[V_{j-1} e^{-\\delta/\\tau} + \\left(1-e^{-\\delta/\\tau}\\right)\\frac{I_{j-1}\\tau}{C}\\right]\n",
    "     e^{-\\delta/\\tau} + \\left(1-e^{-\\delta/\\tau}\\right)\\frac{I_j\\tau}{C} \\\\\n",
    "  &= \\left(1-e^{-\\delta/\\tau}\\right)\\frac{\\tau}{C}\\sum_{k=0}^{j} I_k e^{-(j-k)\\delta/\\tau} \\\\\n",
    "  &= \\left(1-e^{-\\delta/\\tau}\\right)\\frac{\\tau}{C}\\sum_{k=0}^{j} I_{k} e^{-k\\delta/\\tau} \\;.\n",
    "\\end{align}$$\n",
    "\n",
    "In the last step, we exploited the mutual independence of the random current amplitudes $I_k$, which allows us to renumber them arbitratily."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean and variance of the membrane potential\n",
    "\n",
    "The mean of the membrane potential at $t_{j+1}$ is thus\n",
    "\n",
    "$$\\begin{align}\n",
    "\\langle V_{j+1}\\rangle &= \\left(1-e^{-\\delta/\\tau}\\right)\\frac{\\tau}{C}\\sum_{k=0}^{j} \\langle I_{k} \\rangle e^{-k\\delta/\\tau}\\\\\n",
    " &= \\frac{\\mu\\tau}{C}\\left(1-e^{-\\delta/\\tau}\\right)\\sum_{k=0}^{j} e^{-k\\delta/\\tau}\\\\\n",
    " &= \\frac{\\mu\\tau}{C}\\left(1-e^{-(j+1)\\delta/\\tau}\\right)\\\\\n",
    " &= \\frac{\\mu\\tau}{C}\\left(1-e^{-t_{j+1}/\\tau}\\right)\n",
    "\\end{align}$$\n",
    "\n",
    "as expected; note that we used the geometric sum formula in the second step.\n",
    "\n",
    "To obtain the variance of the membrane potential at $t_{j+1}$, we first compute the second moment\n",
    "\n",
    "$$\\langle V_{j+1}^2 \\rangle = \\frac{\\tau^2}{C^2}\\left(1-e^{-\\delta/\\tau}\\right)^2 \\left\\langle\\left(\\sum_{k=0}^{j} I_{k} e^{-k\\delta/\\tau}\\right)^2\\right\\rangle$$\n",
    "\n",
    "Substituting $q = e^{-\\delta/\\tau}$ and $\\alpha = \\frac{\\tau^2}{C^2}\\left(1-e^{-\\delta/\\tau}\\right)^2= \\frac{\\tau^2}{C^2}\\left(1-q\\right)^2$ and , we have\n",
    "\n",
    "$$\\begin{align}\n",
    "\\langle V_{j+1}^2 \\rangle &= \\alpha \\left\\langle\\left(\\sum_{k=0}^{j} I_{k} q^k\\right)^2\\right\\rangle \\\\\n",
    "  &= \\alpha \\sum_{k=0}^{j} \\sum_{m=0}^{j} \\langle I_k I_m \\rangle q^{k+m} \\\\\n",
    "  &= \\alpha \\sum_{k=0}^{j} \\sum_{m=0}^{j} (\\mu^2 + \\sigma_k^2 \\delta_{km}) q^{k+m} \\\\\n",
    "  &= \\alpha \\mu^2 \\left(\\sum_{k=0}^j q^k\\right)^2 + \\alpha \\sum_{k=0}^{j} \\sigma_k^2  q^{2k} \\\\\n",
    "  &= \\langle V_{j+1}\\rangle^2 + \\alpha \\sum_{k=0}^{j} \\sigma_k^2  q^{2k} \\;.\n",
    "\\end{align}$$\n",
    "\n",
    "Evaluating the remaining sum for the modulated case will be tedious, so we focus for now on the unmodulated case, i.e., $\\sigma\\equiv\\sigma_k$, so that we again are left with a geometric sum, this time over $q^2$. We can now subtract the square of the mean to obtain the variance\n",
    "\n",
    "$$\\begin{align}\n",
    "\\langle (\\Delta V_{j+1})^2 \\rangle &= \\langle V_{j+1}^2 \\rangle - \\langle V_{j+1}\\rangle^2 \\\\\n",
    "   &= \\alpha \\sigma^2 \\frac{q^{2(j+1)}-1}{q^2-1} \\\\\n",
    "  &= \\frac{\\sigma^2\\tau^2}{C^2} (1-q)^2 \\frac{q^{2(j+1)}-1}{q^2-1} \\\\\n",
    "  &= \\frac{\\sigma^2\\tau^2}{C^2} \\frac{1-q}{1+q}\\left(1-q^{2(j+1)}\\right) \\\\\n",
    "  &=  \\frac{\\sigma^2\\tau^2}{C^2} \\frac{1-e^{-\\delta/\\tau}}{1+e^{-\\delta/\\tau}}\\left(1-e^{-2t_{j+1}/\\tau}\\right) \\;.\n",
    "\\end{align}$$\n",
    "\n",
    "In the last step, we used that $1-q^2=(1-q)(1+q)$.\n",
    "\n",
    "The last term in this expression describes the approach of the variance of the membrane potential to its steady-state value. The fraction in front of it describes the effect of switching current amplitudes at intervals $\\delta$ instead of instantenously as in real white noise. \n",
    "\n",
    "We now have in the long-term limit\n",
    "\n",
    "$$\\langle (\\Delta V)^2 \\rangle = \\lim_{j\\to\\infty} \\langle (\\Delta V_{j+1})^2 \\rangle \n",
    "  = \\frac{\\sigma^2\\tau^2}{C^2} \\frac{1-e^{-\\delta/\\tau}}{1+e^{-\\delta/\\tau}} \\;. $$\n",
    "  \n",
    "We expand the fraction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle \\frac{x}{2} - \\frac{x^{3}}{24} + \\frac{x^{5}}{240} + O\\left(x^{6}\\right)$"
      ],
      "text/plain": [
       "     3     5        \n",
       "x   x     x     ⎛ 6⎞\n",
       "─ - ── + ─── + O⎝x ⎠\n",
       "2   24   240        "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "\n",
    "sympy.init_printing()\n",
    "x = sympy.Symbol(\"x\")\n",
    "sympy.series((1 - sympy.exp(-x)) / (1 + sympy.exp(-x)), x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We thus have for $\\delta \\ll \\tau$ and $t\\gg\\tau$\n",
    "\n",
    "$$\\langle (\\Delta V)^2 \\rangle \n",
    "  \\approx \\frac{\\delta\\tau \\sigma^2 }{2 C^2} \\;.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How to obtain a specific mean and variance of the potential\n",
    "\n",
    "In order to obtain a specific mean membrane potential $\\bar{V}$ with standard deviation $\\Sigma$ for given neuron parameters $\\tau$ and $C$ and fixed current-update interval $\\delta$, we invert the expressions obtained above.\n",
    "\n",
    "For the mean, we have for $t\\to\\infty$\n",
    "\n",
    "$$\\langle V\\rangle = \\frac{\\mu\\tau}{C} \\qquad\\Rightarrow\\qquad \\mu = \\frac{C}{\\tau} \\bar{V}$$\n",
    "\n",
    "and for the standard deviation\n",
    "\n",
    "$$\\langle (\\Delta V)^2 \\rangle  \\approx \\frac{\\delta\\tau \\sigma^2 }{2 C^2}\n",
    "\\qquad\\Rightarrow\\qquad  \\sigma = \\sqrt{\\frac{2}{\\delta\\tau}}C\\Sigma \\;.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tests and examples\n",
    "\n",
    "We will now test the expressions derived above against NEST. We first define some helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def noise_params(V_mean, V_std, dt=1.0, tau_m=10.0, C_m=250.0):\n",
    "    \"Returns mean and std for noise generator for parameters provided; defaults for iaf_psc_alpha.\"\n",
    "\n",
    "    return C_m / tau_m * V_mean, math.sqrt(2 / (tau_m * dt)) * C_m * V_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def V_asymptotic(mu, sigma, dt=1.0, tau_m=10.0, C_m=250.0):\n",
    "    \"Returns asymptotic mean and std of V_m\"\n",
    "\n",
    "    V_mean = mu * tau_m / C_m\n",
    "    V_std = (sigma * tau_m / C_m) * np.sqrt((1 - math.exp(-dt / tau_m)) / (1 + math.exp(-dt / tau_m)))\n",
    "\n",
    "    return V_mean, V_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def V_mean(t, mu, tau_m=10.0, C_m=250.0):\n",
    "    \"Returns predicted voltage for given times and parameters.\"\n",
    "\n",
    "    vm, _ = V_asymptotic(mu, sigma, tau_m=tau_m, C_m=C_m)\n",
    "    return vm * (1 - np.exp(-t / tau_m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def V_std(t, sigma, dt=1.0, tau_m=10.0, C_m=250.0):\n",
    "    \"Returns predicted variance for given times and parameters.\"\n",
    "\n",
    "    _, vms = V_asymptotic(mu, sigma, dt=dt, tau_m=tau_m, C_m=C_m)\n",
    "    return vms * np.sqrt(1 - np.exp(-2 * t / tau_m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "              -- N E S T --\n",
      "  Copyright (C) 2004 The NEST Initiative\n",
      "\n",
      " Version: 3.3\n",
      " Built: Mar 23 2022 13:33:55\n",
      "\n",
      " This program is provided AS IS and comes with\n",
      " NO WARRANTY. See the file LICENSE for details.\n",
      "\n",
      " Problems or suggestions?\n",
      "   Visit https://www.nest-simulator.org\n",
      "\n",
      " Type 'nest.help()' to find out more about NEST.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import nest\n",
    "\n",
    "\n",
    "def simulate(mu, sigma, dt=1.0, tau_m=10.0, C_m=250.0, N=1000, t_max=50.0):\n",
    "    \"\"\"\n",
    "    Simulate an ensemble of N iaf_psc_alpha neurons driven by noise_generator.\n",
    "\n",
    "    Returns\n",
    "    - voltage matrix, one column per neuron\n",
    "    - time axis indexing matrix rows\n",
    "    - time shift due to delay, time at which first current arrives\n",
    "    \"\"\"\n",
    "\n",
    "    resolution = 0.1\n",
    "    delay = 1.0\n",
    "\n",
    "    nest.ResetKernel()\n",
    "    nest.resolution = resolution\n",
    "    ng = nest.Create(\"noise_generator\", params={\"mean\": mu, \"std\": sigma, \"dt\": dt})\n",
    "    vm = nest.Create(\"voltmeter\", params={\"interval\": resolution})\n",
    "    nrns = nest.Create(\"iaf_psc_alpha\", N, params={\"E_L\": 0.0, \"V_m\": 0.0, \"V_th\": 1e6, \"tau_m\": tau_m, \"C_m\": C_m})\n",
    "    nest.Connect(ng, nrns, syn_spec={\"delay\": delay})\n",
    "    nest.Connect(vm, nrns)\n",
    "\n",
    "    nest.Simulate(t_max)\n",
    "\n",
    "    # convert data into time axis vector and matrix with one column per neuron\n",
    "    t, s, v = vm.events[\"times\"], vm.events[\"senders\"], vm.events[\"V_m\"]\n",
    "    tix = np.array(np.round((t - t.min()) / resolution), dtype=int)\n",
    "    sx = np.unique(s)\n",
    "    assert len(sx) == N\n",
    "    six = s - s.min()\n",
    "    V = np.zeros((tix.max() + 1, N))\n",
    "    for ix, vm in enumerate(v):\n",
    "        V[tix[ix], six[ix]] = vm\n",
    "\n",
    "    # time shift due to delay and onset after first step\n",
    "    t_shift = delay + resolution\n",
    "    return V, np.unique(t), t_shift"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A first test simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu = 0.00, sigma = 111.80\n",
      "\n",
      "Dec 01 11:25:56 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:56 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 1002 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:56 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 1002\n",
      "    Simulation time (ms): 50\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:56 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 1.0\n",
    "mu, sigma = noise_params(0.0, 1.0, dt=dt)\n",
    "print(\"mu = {:.2f}, sigma = {:.2f}\".format(mu, sigma))\n",
    "\n",
    "V, t, ts = simulate(mu, sigma, dt=dt)\n",
    "V_mean_th = V_mean(t, mu)\n",
    "V_std_th = V_std(t, sigma, dt=dt)\n",
    "\n",
    "plt.plot(t, V.mean(axis=1), \"b-\", label=r\"$\\bar{V_m}$\")\n",
    "plt.plot(t + ts, V_mean_th, \"b--\", label=r\"$\\langle V_m \\rangle$\")\n",
    "plt.plot(t, V.std(axis=1), \"r-\", label=r\"$\\sqrt{\\bar{\\Delta V_m^2}}$\")\n",
    "plt.plot(t + ts, V_std_th, \"r--\", label=r\"$\\sqrt{\\langle (\\Delta V_m)^2 \\rangle}$\")\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"Time $t$ [ms]\")\n",
    "plt.ylabel(\"Membrane potential $V_m$ [mV]\")\n",
    "plt.xlim(0, 50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Theory and simulation are in excellent agreement. The regular \"drops\" in the standard deviation are a consquence of the piecewise constant current and the synchronous switch in current for all neurons. It is discussed in more detail below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A case with non-zero mean\n",
    "\n",
    "We repeat the previous simulation, but now with non-zero mean current."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu = 50.00, sigma = 111.80\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:57 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 1002 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 1002\n",
      "    Simulation time (ms): 50\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 1.0\n",
    "mu, sigma = noise_params(2.0, 1.0, dt=dt)\n",
    "print(\"mu = {:.2f}, sigma = {:.2f}\".format(mu, sigma))\n",
    "\n",
    "V, t, ts = simulate(mu, sigma, dt=dt)\n",
    "V_mean_th = V_mean(t, mu)\n",
    "V_std_th = V_std(t, sigma, dt=dt)\n",
    "\n",
    "plt.plot(t, V.mean(axis=1), \"b-\", label=r\"$\\bar{V_m}$\")\n",
    "plt.plot(t + ts, V_mean_th, \"b--\", label=r\"$\\langle V_m \\rangle$\")\n",
    "plt.plot(t, V.std(axis=1), \"r-\", label=r\"$\\sqrt{\\bar{\\Delta V_m^2}}$\")\n",
    "plt.plot(t + ts, V_std_th, \"r--\", label=r\"$\\sqrt{\\langle (\\Delta V_m)^2 \\rangle}$\")\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"Time $t$ [ms]\")\n",
    "plt.ylabel(\"Membrane potential $V_m$ [mV]\")\n",
    "plt.xlim(0, 50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We again observe excellent agreement between theory and simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Shorter and longer switching intervals\n",
    "\n",
    "We now repeat the previous simulation for zero mean with shorter ($\\delta=0.1$ ms) and longer ($\\delta=10$ ms) switching intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu = 0.00, sigma = 353.55\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:57 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 1002 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 1002\n",
      "    Simulation time (ms): 50\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n"
     ]
    },
    {
     "data": {
      "image/png": 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ptnOnBYUNG6z38q5dNtjczp2551wACxBJSZZbGD/ex9NxzuWrKEVSfkcprdLTrZnrMcdYD+Y9e2DYMOunULOm9ZO49lrb98gjbayn336z4TxeesmDhXMu6rxIqrRaujQ0PeUvv1hl9cMPW7CoXt2GcB482Cqra9e2nIhzzsWQB4zSKjgl5eLFsHIlnHaadXj76CMbQ6lfP+trcfjh8U2nc67C8IBRWs2caXUSxx1nQ3O8+qrNAX3EETZxTp8+8U6hc66CKTRgiEi9MI6Tqarbip8cB9jYT6+/DtdcE1rXowfccAPce68VQTnnXAkLJ4exLvAoaCCfBKBJVFJU0f3xh/XQPvpoK27q2dOmDT3sMHjyyXinzjlXgYUTMJap6okF7SAiC6KUnopr506r5B4zxoYZb9HChu/o08daSHmuwjkXZ+EEjNOitI/Lz3ffwfnnh/pW1K5tc2E//rjNNe2jtDrnSoFwGuv/W0TOKGgHVd0XpfRUHGlpNpy3iLWAqlnTipwaN7YJhmbMgJtv9mDhnCs1wslh/IQFjcOBN4CJqrowpqmqCKZPh++/t9fXXWfDebdqZZXbBx1kPbqdc64UKTSHoapPqeppQFdgC/CiiCwTkbtFxAcpitSuXTZ8+H33Qf36ltNo3NhyF6rWjNaDhXOuFAp7/AhVXaOqjwQqwC8GBgDLYpay8qp/fzjjDFi0yCq477zTZpXbvt0mFXLOuVIq7IAhIlVE5HwRmQB8CKwELohZysqjb7+1SYwuvNDmnP7kE3j0Uetv8corPsOcc65UC6fj3tnARUAfYDbwOjBcVXfHOG3lzyuvQI0aNvvdP/9pExz9/e/w4INeue2cK/XC+Ul7B/AacKuqFjAJtCtQRga88471q6hZ0zrk1apldRkeLJxzZUChAUNVzyyJhJR7X38N69db/QVA7972cM65MiKSOowkEXlXROaLyCIRWSwiiyI5mYj0EpEVIpIsIn/PY/shIjJVRH4QkaUicmUkxy/VXnvN+lfccovVYzjnXBkTSS3rBOBvwGIgM9ITiUgCMBo4G0gB5ojIe6r6Y5bdrgN+VNXzRaQBsEJEJqhqWqTnK1UWLIAXXrDX3btDly7xTY9zzhVBJAFjo6q+V4xznQIkq+oqABF5HegHZA0YCtQSEQFqYv0+0otxzvh691146y2b00IVEhNtuUqVeKfMOeciFknA+JeIvAB8CqQGV6rqO2G+/0hgbZblFKBjjn2eBt7DRsetBQxV1YhzM6XC6tUwcGBouVYt6919yCFxS5JzzhVHJAHjSqANUIVQkZQC4QaMvJoCaY7lnsBC4CygBfCJiHylqjuyHUhkODAcoEmTUjqq+v/+Z88PP2z9L26+GY46Kr5pcs65YogkYJygqscX41wpQNY7ZmMsJ5HVlcDDqqpAsoj8ggWp2Vl3UtWxwFiApKSknEEnvlJT4YIL4IMPbFyo22+Pd4qccy4qwm4lBXwnIscW41xzgJYi0kxEqgIXYsVPWf0KdAcQkUZAa2BVMc5ZsjZvtv4VH3xg06vOnQtz5sQ7Vc45FxWR5DA6AZcHfvWnYkVMqqrtwnmzqqaLyPXAR9gMfeNVdamIXB3YPga4D3hJRBYHjn+7qm6KII3xo2pzbs+cCc2bW0e9ypWtots558qBSAJGr+KeTFWnAdNyrBuT5fU64JzinicuVqywnMWwYTYR0nvvWWe9mjXjnTLnnIuKsAOGqq6JZULKvI8/tufjjoMRI2DkSJsgyTnnyolC6zBEZH409in3pk+HY46Bn36yQPHPf8Y7Rc45F1Xh5DASCxkCRICK3blg40YbqvyWW6wZ7Z49PlS5c67cCeeu1iaMfSruzD/799v8FunpcMoptu6gg+KbJueci4FwRqv1uouCfPQRfPYZ1Ktn9RYDBvhw5c6Faf/+/aSkpLBv3754J6Xcql69Oo0bN6ZKFIYk8nKT4nrxRZsUacsWGzvKg4VzYUtJSaFWrVo0bdoU8f+dqFNVNm/eTEpKCs2aNSv28SLpuOdy+vFHmxQpLQ0uvthHoXUuQvv27aN+/foeLGJERKhfv37UcnBFChgicqyInCsijaOSirLq/vshIcFGn33ooXinxrkyyYNFbEXz+hY1h3EPNprscBF5OWqpKUuWL4eJE+Hkk60JbWkdBNE556KkqHUYn6jqm8Cb0UxMmfLII9Ya6r33oEGDeKfGORcDnTt3ZufOnVSuXJm5c+fGOzlxV9SAcbqI9AI2A8tU9YkopqlseP99y10cemi8U+Kci5Gvvvoq3kkoVYoaMJao6r9FpDJwXDQTVCakpNh4UUuXhgYZdM65cq6odRjnicgNQHNV/SGaCSoTRo2y52uv9WDhXBmXnJzM8cdnn+onNTWVZs2a8eOPP+bzroopnLGk8urpPRT4CRgoIs9HPVWlWWYmjBljraNuuy3eqXHOFVPz5s1Zu3YtmZmh2aDHjh1L165dOfbY4kwBVP6E8/N4moh8AYxU1V8BVHU9MD3wqFiGDIGdO2HoUDj44HinxjlXTJUqVaJJkyasXr2a5s2bs3fvXh5//HG++OKLeCet1Al3LKmrgJkiMgV4QFU3xjZZpdSGDTB5Mhx2WGjObudcVIwYAQsXRveY7dvDk08Wvl9iYiLLly+nefPmjB49mr59+9K0adPoJqYcKLRISlXTVPW/QCI2L/f3InKviNSKeepKm1desUruzz+HqlXjnRrnXJQkJiayYsUKdu3axejRo/mnT0+Qp0gmUNoH/FtEngVuAuaLyHOq+u+Ypa60GT8e2rWDNuEM4Ouci0Q4OYFYSUxM5LPPPuOpp57ikksuoVGjRvzxxx8MHTqUPn36sHTpUk4//XQ++eQTRo4cSdu2beOX2DgKu5WUiDQN9L34C9AE2Ak8GKuElToPP2xjRzVsGO+UOOeiLDExkdmzZzN+/Hj+9re/AbBgwQIGDhzIbbfdxvbt2xk2bBiDBw9mzZqKO4B3OK2kFonIFmAycAVQB/gMuByoGBNWr1sHd94JlSrBs8/GOzXOuShr3bo1ixcvZvjw4RxyiM0Ht3DhQnr27Mn+/fupX78+lSpVYsmSJbma4FYk4RRJDQBWqarGOjGl1n/+Y3UXF19s07A658qVatWqkZ6enm1dcnIyrVq1YtGiRSQmJgKwevVqmlTgceOkrMeBpKQkjfkYL4cdBuvXw6JFUIF/XTgXbcuWLTtwM3axk9d1FpF5qpoUyXF8PozCLF9uwaJ5cw8WzrkKzQNGYd59156nTIlvOpxzLs48YBRm0iQ45RSooM3onHMuKJxWUjtFZEcej50isqMkEhk3P/wA8+dDixbxTolzzsVdoa2kVLXi9egOuv9+e77wwvimwznnSoGIxuYWkbpAS6B6cJ2qfhntRJUaH30E1atD377xTolzzsVdJD29/wJ8CXyEzen9ETAykpOJSC8RWSEiySLy93z26SYiC0VkqYjMjOT4UfXllzYqbadOcUuCc86VJpFUet8EnAysUdUzgROBsEetFZEEYDRwLnAscJGIHJtjnzrAM0BfVT0OGBxB+qIrONfFvffGLQnOOVeaRBIw9gUGIEREqqnqcqB1BO8/BUhW1VWqmga8DvTLsc/FwDtZ5t3YEMHxo2fbNli8GJKS4LTT4pIE55wrbSIJGCmBHMBk4JPA3BjrInj/kcDarMcLrMuqFVBXRL4QkXkiclkEx4+e55+HPXvs2TlXIZx11llFnq5169atDBgwINZJjLtIhjcPXo2RIvI5cAiRzbgneR02j/R0ALoDNYBvReQ7VV2Z7UAiw4HhQPTHdVGFJ56wYczbt4/usZ1zpdLSpUupX79+tulaK1Wy39PhTNdat25dtmzZwubNm6lfv35JJbvEFanjnqrOVNX3AkVL4UoBjsqy3JjcOZQUYLqq7lbVTVgl+wl5nH+sqiapalKDBg0iTX7BPv8c/vgjusd0zpVqU6ZMoX///tmmawUOTNc6cuTIQo/Rp08fpk6dGtuExlmhOQwR+VpVO4nITrLnCARQVa0d5rnmAC1FpBnwG3AhVmeR1RTgaRGpDFQFOgL/CfP40fHoo/Z8zTUlelrnHHTrlnvdkCFw7bVWSty7d+7tV1xhj02bYNCg7NvCnZZ72rRpvP/++0DRp2vt168ft99+O1dccUV4Jy2Dwum41ynwXKwOfKqaLiLXY81xE4DxqrpURK4ObB+jqstEZDqwCMgEXlDVJcU5b4SJhK++AhEYHL8GWs65krN3717S0tKoU6cOEJqutUuXLowePZrvvvsurOO0bt2aFStWxDCl8Rd2HYaIPKKqtxe2riCqOg2YlmPdmBzLjwGPhXvMqFq3zn7GtG4N5bgc0rnSqqAcwUEHFbz90EPDz1FkVaNGDUSEXbt2UbNmzTynawUKnbJ1zZo1NGvWLPIElCGR1GGcnce6c6OVkFIh+G07t3x9LOdcwXr27Mn06daGJ6/pWqHwKVunTJlCv345ewqUL+EMPniNiCwGWgemaw0+fgEWxz6JJeinn+z5zjvjmw7nXInq168fkydPBvKerhUKn7J16tSp9C3nwwiFUyT1GvAh8BCQdTiPnaq6JSapipf58yEx0YujnKtgOnTowOLFi0lPT89zulYoeMrWrVu3kpqayuGHH17SSS9RYU/RKiLVgYFAU7IEGlWN69gZUZuiddcuqFsXTj8dZsZvCCvnKhKforVkRGuK1khGq50MbAfmAamRnKRMePttSE+HAjrnOOdcRRZJwGisqr1ilpJ4mzTJnvv0iW86nHOulIqkldQsETm+8N3KIFWYNcteew7DOefyFEkOoxNwpYiswoqkgj2928UkZSXpl19gyxaoVAmiPTaVc86VE5EEjPLbOSEzE44+2gJG5YgmIXTOuQojkiKpX4HOwOWqugYbV6pRTFJV0po1g4wMH53WOecKEEnAeAY4DbgosLwTm0GvbFOFceMgJQUuuqjw/Z1zroKKpPylo6qeJCILAFR1q4hUjVG6Ss6KFXDVVVC1KpTzbv3OOVcckeQw9gfm5VYAEWmAjShbtn3+uT23bWtBwznnXJ4iyWGMAt4FGorIA8Ag4K6YpKokffqpDWfuc3c75/IhkteEodEX7sgb8RJ2DkNVJwC3YWNK/Q70V9U3Y5WwEqFqw4CoQocO8U6Nc66Uuv3220lPT0dVY/oo7YoyH8byPNaVTWvW2DRdAJ06xTctzrlSKXgzT0hIiHdS4q5iz4fRoAF06WLPxxwT79Q450qh2bNnc/LJJ0f8vs6dO9O+fXuSkiIa369UC2dO72uAa4HmIrIouBqoCXwTw7TF3kEHwapVcOaZVo/hnHM5fPzxx4wYMSLi93311VfRT0ycVez5MP7zH+t/0blzvFPinCuldu7cSa1ateKdjFKh0CIpVd2uqqtV9SKgDnB+4HFUjNMWW6mpcHug+qVLl/imxTlXKq1Zs4amTZsW+ziTJ09m2LBh9OvXj48//rj4CYuTsOswRORGYALQMPB4VURuiFXCYm7BApv/4uCDrQ+Gc87lMHXqVM4///xc6999911EhOXLD7QBIjk5+cB0rUGpqak0a9aMVq1a8fzzz/PSSy/xxhtvxDzdsRJJpfdfsN7ed6vq3cCpwLDYJKsEfPedPXfqZIMOOucqtP379+da9+uvv3LUUbkLUyZOnEhSUhKvv/76gXXNmzdn7dq1ZGaG+jOPHTuWrl27cmxg2oT777+f6667LgapLxmR3CkFyMiynBFYVzZ9+qk99+4d33Q45+Luyy+/pFWrVuzatevAuh07dnDIIYfk2nfXrl3MnDmTcePGMXHixAPrK1WqRJMmTVi9ejUAe/fu5fHHH2fkyJGoKrfffjvnnnsuJ510Usw/T6xE0tP7ReB7EXk3sNwfGBf1FJWUOXPs+cwz45sO55wZMQIWLozuMdu3hyefLHS3I444gjZt2jB9+nQGDRoEwPTp0+nVK/cko5MnT6ZHjx60a9eOgw8+mPnz5x8IAomJiSxfvpzmzZszevRo+vbtS9OmTRk1ahQzZsxg+/btJCcnc/XVV0fzU5aYSHp6PwFcCWwBtgJXquqTMUpX7PXoAXXrwnHHxTslzrk4O+aYY7jsssuYMmXKgXXz58+nQx4jQEycOJEhQ4YAMGTIkGy5jMTERFasWMGuXbsYPXo0//znPwG48cYbmTdvHmPGjCmzwQIiy2GgqvOB+TFKS8lRha++grPO8voL50qLMHICsdS7d29GjBhBeno6IkLlPCZT27x5M7Nnz+add94BYOjQoXTt2pVHH30UESExMZHPPvuMp556iksuuYRGjcrHlEFBkQwNUh3rwNcJG7H2a+BZVd0Xo7TFztix8OuvcPPN8U6Jc66UOOSQQzj++OP58ssvSUhI4Iwzzsi1z6RJk+jduzfVqlUDoFmzZhx22GF8/fXXdO7cmcTERB5++GFmzJjB/Pll/7d1TpHkMP6HTZr038DyRcArwOBoJyrmXnnFnnv0iG86nHOlSr9+/ZgyZQp169blH//4R67tEydOZNGiRdn6ZmzevJnXXnuNzp0707p1axYvXswDDzxwoML8jz/+YOjQofTp04elS5dy+umn88knnzBy5EjalrEm/ZEEjNaqekKW5c9F5IdITiYivYCngATgBVV9OJ/9Tga+A4aq6qRIzhGW5cuhShUINHVzzjmAvn370q1bNy688MIDuYisvvjiiwLfX61aNdLT07OtW7BgAQMHDuSmm26if//+DBs2jDp16rBmzZoyFzAiKcBfICKnBhdEpCMRjCUVmHxpNDZg4bHARSKS644d2O8R4KMI0ha+tDTYsgWOPNLHj3LOZXP00UdTu3Zt2rRpE7VjLly4kJ49e7J//37q169PpUqVWLJkSa5OfmVBJAGjIzBLRFaLyGrgW6CriCzOMihhQU4BklV1laqmAa8Dec2JegPwNrAhgrSF74cfrNL7hBMK39c5V+EMGzaMPn36RO14ycnJtGrViqVLl5KYmAjA6tWradKkSdTOUVIiKZLK3SA5MkcCa7Msp2BB6AARORIYAJwFRD6ecDi+/96eu3WLyeGdc2Xb9ddfH9XjjRtn3dXat29P+/btAXglWI9axoQdMFR1TTHPlVf5T84ppp4EblfVjIKmRBSR4cBwIPIoHTzuwIGRvc855yq4iPphFFMK2Ue4bQysy7FPEvB6IFgcCvQWkXRVnZx1J1UdC4wFSEpKimxew7lzoWFDyGN8GOecc/kryYAxB2gpIs2A34ALgYuz7qCqzYKvReQl4P2cwaLY3nkHjjjCK7ydcy5CkQxvLiLyJxG5O7DcREROCff9qpoOXI+1floGvKmqS0XkahEpmb7ye/fCjh2Qx4BizjnnChZJDuMZIBOrkL4X68T3NhFUTqvqNGBajnVj8tn3igjSFp5gG+p27aJ+aOecK+8iCRgdVfUkEVkAoKpbRaRqjNIVGzNn2nMeXf6dc84VLJJ+GPsDneoUQEQaYDmOsiM4tsvZZ8c3Hc45VwZFEjBGAe8CjUTkAWzwwQdjkqpY2bEDqlWzSm/nnHMRiaQfxgQRmQd0D6zqr6rLYpOsGFH14ijnXEQK6hNWmqlG1uMgHJG0kqoGnAQcAtQHBgdbTJUJqrBsGQS65jvnXGHWrl3LG2+8gaqWuUcsRFLpPQXYDswDUmOSmlhKToadO2HbtninxDlXRnz00UcMHlz2ZnCIlUgCRmNVLe54UvEza5Y9ew9v51yYtm/ffmBeCxdZpfcsESl74/EG/RCYuiMw+JdzzhVk165d1KpVK97JKFUiCRidgHkiskJEFkUwrHnpsGKFPZ96asH7OeccVhx1zjnnxDsZB0yePJlhw4bRr18/Pv7447ikIZKAcS7QEjgHOB84L/BcNvz6qz0ffXR80+GcKxN++eWXbFOxApx11lkHZtTbu3cvXbt2JSMj48D2d999FxFh+fLlB9YlJyfnmiwpNTWVZs2a8eOPP+Z7/rS0NLp06XLgfP379+f555/npZde4o033mDr1q0MGDCguB8zImEHDFVdk9cjlomLqsqVoX79eKfCOVdKZWaG+iFnZGRQuXL2Kt6lS5dSv379A+vHjx/PwIEDSUhIOLDPxIkTSUpK4vXXXz+wrnnz5qxduzbb8ceOHUvXrl05toBpoqtWrUr37t154403sq2///77ue6666hbty5btmxh8+bNRfvARRBJDgMRqSsip4hIl+AjVgmLuoQESEqKdyqcc6VMZmYm99xzD3fdddeBdbNmzeL000/Ptt+UKVPo37//geUJEybQr19o0tBdu3Yxc+ZMxo0bx8SJEw+sr1SpEk2aNGH16tWA5Uwef/xxRo4cWWja+vfvz4QJEwDrV3H77bdz7rnnctJJJwHQp08fpk6dGulHLrJI+mH8BfgSG232nsDzyNgkK8pUrUjKW0g553IQEf7617/y6aefHlg3d+5cTj45+7iq06ZNOzB1a1paGqtWrcpWZDV58mR69OhBu3btOPjgg5kfHIoISExMPFBMNXr0aPr27ZuruCsvbdu2Zc6cOQD897//ZcaMGUyaNIkxY2zM1n79+jF58uSifOwiiaRZ7U3YyLTfqeqZItIGCxyl3++/w8aN9uycK73ymjp5yBC49lrYswd69869/Yor7LFpEwwalH1bcITqAogItWvX5qijjiI5OZljjjmGzMzMbD289+7dS1paGnXq1AFg06ZNB14HTZw4keHDhweSPISJEyceyAkkJiayYsUKunTpwujRo/nuu+8KTRdAQkICVatWZefOndx4443ceOON2ba3bt2aFcEGPSUgkiKpfaq6D6zXt6ouB1rHJllRtnChPXuFt3MuH/369WPKlCmsXLmS1q2z39pq1KiBiLBr164Dy/v27TuwffPmzcyePZtevayr2tChQw/0EIdQDuOpp57ikksuoVGjRmGnKzU1lerVq+e5bc2aNTRr1izPbbEQSQ4jRUTqAJOBT0RkK7mnWC2dFi+251at4psO51zBCsoRHHRQwdsPPTSsHEV++vTpwwUXXECNGjW48sorc23v2bMn06dPZ9CgQdStW5eMjAz27dtH9erVmTRpEr1796ZatWoANGvWjMMOO4yvv/6azp07k5iYyMMPP8yMGTOyFVX98ccfDB06lD59+rB06VJOP/10PvnkE0aOHEnbtm3ZvHkzDRo0oEqVKnmmecqUKdnqUWItrByGWN7sRlXdpqojgbuAcUD/2CUtioJZNp84yTmXj7p161KpUiV+//13atSokWt7zvqCc845h6+//hqw4qipU6fStGnTA49ly5bx2muvAVZ0tHjxYoYPH56t5/iCBQsYOHAgt912G9u3b2fYsGEMHjyYNWusAernn39O77yK4QKmTp1K3759o/HxwxJWDkNVVUQmAx0CyzNjmaioC1x8TjwxvulwzpVq5513Xr69uzt06MDixYtJT0+ncuXKXH/99TzxxBP06NGDLwrJ2VSrVu1Af4qsFi5cyIABA9i/fz/169enUqVKLFmyhGHDhgHw2muv8dBDD+V5zK1bt5Kamsrhhx8e2YcshkiKpL4TkZNVdU7MUhMrBx0E1atDjkoq55zL6rLLLsvWryKnH4JDDAEnnngiZ555JhkZGQW+pyDJycm0atWKRYsWkRgYSXv16tU0adKEtLQ0+vfvn6s+Jahu3bp8+eWXRTpvUUm4w+CKyI9YJfdqYDcgWOYjruU8SUlJOnfu3IJ36tsXVq+GRWVnJBPnKoJly5YduFG62MnrOovIPFWNqHNaJDmMcyM5cKmyahU0bhzvVDjnXJkWScBYD1yLDUKo2BStz8YiUVH3449QRmfNcs650iKSgPE/YCfw38DyRcArQOmeXWTDBuvpfeSR8U6Jc86VaZEEjNaqekKW5c9F5Id89y4tFiywZ++051yppKpldt7ssiCa07VG0tN7gYgcmExCRDoC30QtJbGycqU9t2gR33Q453KpXr06mzdvjtkc1BWdqrJ58+Z8e4pHqtAchogsxuosqgCXicivgeWjgfwHcy8tAiNE0rx5XJPhnMutcePGpKSksHHjxngnpdyqXr06jaPU6CecIqnzonKmeDn4YHs+4YSC93POlbgqVaqU6FhIrngKDRhlapKkvKhCpUqew3DOuWKKZD6MJBF5V0TmF3VObxHpFZgTPFlE/p7H9ksCx14kIrNEpPjZgp9+sh7eReyJ6ZxzzkTSSmoC8DdgMZBZyL65iEgCMBo4G0gB5ojIe6qatR7kF6Crqm4VkXOBsUDHSM+VzVdfwe7dxTqEc865yALGRlV9rxjnOgVIVtVVACLyOtCPLBXnqjory/7fAcWvqdm5E/IYedI551xkIgkY/xKRF4BPgdTgSlV9J8z3HwmszbKcQsG5h/8DPsxrg4gMB4YDNGnSpOCz7tsHEUxW4pxzLm+RBIwrgTZY89pgkZQC4QaMvHrm5Nn4WkTOxAJGp7y2q+pYrLiKpKSkghtwp6dD7dphJtE551x+IgkYJ6jq8cU4VwpwVJblxuQxY5+ItANeAM5V1c3FOB9kZlorKQ8YzjlXbJH09P5ORI4txrnmAC1FpJmIVAUuBLLViYhIEyzHcqmqrizGuczOnfZ86qkF7+ecc65QkeQwOgGXi8gvWB1GRPNhqGq6iFwPfAQkAONVdamIXB3YPga4G6gPPBMYWyY90vHas9m+3Z7bti3yIZxzzplIAkav4p5MVacB03KsG5Pl9V+AvxT3PAf89ps9ex8M55wrtkiKpH4FOgOXB3p/K1C6mx8tXGjP63JVlTjnnItQJAHjGeA0bB4MsLkxRkc9RdG0fr09l+Ak6c45V15FUiTVUVVPEpEFAIHe2FVjlK7o2LDBno84Ir7pcM65ciCSHMb+wPAeCiAiDSjCECElatMmez7qqIL3c845V6hIAsYo4F2gkYg8gM3p/VBMUhUtW7bYswcM55wrtrCLpFR1gojMA7oHVvVT1eWxSVaUtGgBM2dCzZrxTolzzpV54cy4l3PAweAQHz1FBFXtG/1kRUmNGnDQQeDzBTvnXLGFk8M4DRs0cCLwPXmPCVU6paVB1dJdL++cc2VFOAHjMGwOi4uAi4EPgImqujSWCYuK1FSoVi3eqXDOuXKh0EpvVc1Q1emqejlwKpAMfCEiN8Q8dcXlOQznnIuasCq9RaQa0AfLZTTFWkyFO6x5/HgOwznnoiacSu+XgbbYZEb3qOqSmKcqWjyH4ZxzURNODuNSYDfQCrhRQi2OgqPVlt7JJjyH4ZyLk8xM6zu8aRMcW5yJIUqRQgOGqkbSua908RyGc66E7N4NTzwB9etDcjK8/z789JNte/JJuOEGqFR276ZAZD29y560NM9hOOfy9PbbcN11sHZt5O9Vhc8+g6FD4fTTYeRIqFsX7r7bjjlqFBx6qC2LwIgR0K1baMaFsiqSwQfLntRU7+XtXBmydy988QWcdBI0apR7280320335JPhrrvsRv3aazB3bmQzMa9cCX/6E+zbZ6/ffBPq1Amvj+9dd1mwWbXKbjEA334LhxwCL78MzZpZ8AiOSPSnP8HTT8Ozz9rnWrrUgkmZpKpl+tGhQwfN1wknqPbrl/9251ypsG+f6siRqs2aqYLqUUepbtpk2zZsUB00yNZnffTrF3rdrZvqiBGqr7wS3rlatlStX191+PDQMe6+u+D3ZWSoPvZY9jS8+KLqjh2qjz+uumBBwe+fM0e1cmXVyy8vPI0lAZirEd5v437DL+6jwIDRpo3q4MGRXUXnXIlKTVW94AK7G516quqdd6pWqaLap4/q+vWqJ5+smpBg/87Dh2ffP+dDRHXXrvzPNWdOaN/331fdv99u+i1b2jmSklRfesn23b07+3tHjgy995lnVGfPjvyz3nGHvf+KKyJ/b7R5wMipeXPVP/0psqvonCsxmZmqPXrYneixx0Lrn3wydHNOSFB9773s70tNDW0fPNgCzbvv2vITT+R9rkWLVBs1sn3atbNzB61fr3r22aFjXnSRPScmqn7+uQWWRo1Uzz/fXhfVvn2qffvasVesKPpxosEDRk5HHqn65z9HdhWdK0UyM1XHj1ft31+1VSvVjh1VN2+Od6qiY+lS1YcesrvQI49k35aRYYHkrLNUf/gh//cvX27XKCPDns89V7VqVdVnn1WdODEUFDIzVdu3Vz38cNW5c1W3b8/7mPv2WVAA1WOOUW3aVLVGDbuVgOrbbxf/c69ZY8e67rrsQaukecDIqUED1WuuiewqOhdj8+erXnyx/SIuzMSJmqvYpVEjK1opq156Kfuv+cRE1b17c+9XlJvpxo2hmzuonnaa3ZgvvdSWn3228GOkpqrec48Fqs8/V61Vy4LHo48WL3eRVbBO5oILVH/9NTrHjJQHjJxq11a96aaILmJx7NoV318MrvTaty/03K6d/efVrm2/kvfvtyKRnCZNsuKYE09UTU+3G1mword6ddU33lD9/vuy852bO1d1wgT7TMEb+rPPhq5NtGzYoDp9ut2MGzSw6wx2HXfsiPx4mZnRv8aZmar33Wfp6tIluscOlweMnKpXV73ttsiuYiGefVZ12DDVVatsOT1d9V//Ur3/fjvdgAH5/wpJTrbKrkcftZtBWflHd6q//67600+Rvy8z037hVqtmRSxHHGH/dX/5S+im2bJlaF1Ghr1v7Fh7T4cO2Yug0tNV162zoqng+6+9Nvs59+6N36/WnDIzVb/7TrVnz1B6a9VSXbJE9dtvSy4d27aFrm1p8vjjdk2KUoFeXB4wssrMtCYTd94Z+ZXMx/LloV9Hhx9uRQpTp2quIoPBg0NNArPq0yf7ftWrW/l0UX71uNhas8ZuzKr2VWraVA9Uhi5aFP5xXnzR3te5s/3SPfNM1VdftRv/Aw+o1q1rbTP697f9evSwfcFahS9fnvdxU1JCgQZUGza0Yp577lE9+GD76q9cWdyrUDyrV6s2aWLpq1dP9d577XoEf2w5q0upXVt16NCSP7cHjKz277ePd999kV/JPEycaDf4atVUJ09Wbds2+83/r3+1P36XLrZcs6blJjZvthvOJ5/Y+ocftl87wZtC8J/p+utV33orKkl1xfTkk3bDTUiw17Nm5Q70X39d8DEyM61lz0EHqXbqlP+v2/T0UJHHo4/azb5ePftFvm1b4WlNS1O9+mrVww7L/cPlmWci/+zR8tFHoXQ89VT+lcxO9dZb7bu2erUtv/WW9SnZv1/1hRdUTzrJKv8bN7YfnWlp0TmvB4ysdu3SPJtfFMHu3fZLsGPH0C++tLRQW/CXXw7tu3evBZSePa0teZcuoWKIxo1V9+wJHXPjRsuhnHNO6J9r4MD8/7l++031wQct0/TQQ9Ev+61ofvlF9bPPQsu7d6tOmWL/vGefnb3YB0LFUsHOZf36heoepkyxfgJjxlgQuOee0PtmzAg/Tfv22fsjlZpq36f337cy/KOOsorVeNi40f5fQPWSS+KThrLk11+tQ9/AgfbIWnQHdv9o00b19NNt+fnno3NeDxhZbdliH+/JJyO/kgErV9o//nHH2aG+/DL79tRU1YUL83//Aw+E/vjXXms3qPykplqOJNgK5n//s+Kq7t2tYnTs2NAXKPgYOTLv1iUuPMFA/t139gOgWzdbrlLFvj5791ozyksuUR01KvS+RYusty5Ym4qUFGt6Gfy7VKmiB4otH3ooPnVV115rabjqKtWZMy0Y3nyzfZ+L8gs1M9OOddhhFojyO0ZmphXbVami+s03/qMmXLfcEvr+3Hef6l13WYX9gw+GcqeZmdbfJCFB9fXXs79/2jS73kHhfOc8YGT1++9a1Hz50qXWHC/rzblv38j/8TMy7NfAhAnhvyfnr9qsLUq6d7dfuFnL1C+7LLI0OcvqZy0SzPqoUSP8osFLL7Ub47HHWtv/n36yv/VNN6m++WZ8K1k3bbKmoMHP1aZN6PXJJ1tl+vDh1ogj64+O99+3m1ROM2dqtgr6hx6yX8MXXWSvg/Vwo0bZ9nvvLZnPWV7s22d/i8Lqx4LF2QkJ9gMnKcl+8AT/tjfcYPeGFi3sx86VV1qOMy+lPmAAvYAV2DSvf89ju2Cz+SUDi4CTCjtmvgEj2Dtm3LiC/wI5TJqkB+oVHnnEfj1+9FHBww1E02+/Wa5l+nQr2vr5Z9Ubb7S4l7Wo4uOPQ1+S0liJuHu3BcvRo628vzS1UHnuObtuZ51ldVOjRql27Rr5TW7z5lBO4+mnY5HS4ps2LfQ9OeSQUPFn1hxRsHht/PjQcqVKqh98YK14+va1XG/DhvZ3DdbTZX0MHWrFewkJtn9p+nuXN9u2Wb1Y8NqL5P3jB6xCPb9cXqkOGEAC8DPQHKgK/AAcm2Of3tjMfoLNH/59YcfNN2D89JMq6IhDX9EhQ1R//DG0afZsq2T+3//sH+DWW60MOuvAYvGsMAxXSor9wm3dOv7DDGS1YUPuStgzzrBintKgWzfV44+PXlFROJXT8bR2reUmZs2yoqQNGyxX0b177sBRp451pMu6rmZNa921eLEd74knQtsuvdSakgeXExO9grukZGZar/Tu3a0eJC3N/seWLg3loAcMyP/9RQkYYu+LPRE5DRipqj0Dy/8AUNWHsuzzHPCFqk4MLK8Auqnq7/kdt/UhjfW5NpfkWn/Q3s2csngcg3mTSQwmIcGGG05Lg/XrISMj7+PVrw+33w633gqbN8OgQbn3ueYaGwd/7Vq49NLc22+5Bc4/H1asgKuuyr39zjuhRw9YuNDGyc/pwQdtjP1Zs+COO3Jvf/JJaN8eZsyAyy+HdevgoIOgXj0bYvntt6F1a5g6FR5/PPf7X3nFrsUbb9iQyzlNmmTDL7/0kj1ymjbNzvfMMzYsdE4DB8JNN8GFF9o12LkTfv4ZGjaEE0+EDz+0/e67Dz79NPt769e39AP84x82bHRWjRvDq6/a6xEj7Bpm1bIl3HgjtG1r137ePBsOOzPTZj1r2xaef94ms/njD0hJyf7+006DhwLfyAsusO9AVt272/DWAOeea0NuZ3XeefbdAZv/IKchQ+Daa2HPHujdO/f2K66wx6ZNJffdU4Vt22zqmEcftXRPnmzXv3p1+04FPfkkHHkkXHwxbN9u34O0NFi+HKpUgbfegi5d4vfd++ILe/73v20Co6xq1Ijtd69VKxg71l4PH27DpmfVvr1dP7Ahz2P53Tv1VBtG/ZhjQn+/nN+9mTNlnqomEYGSnA/jSCDrVCUpQMcw9jkSyBYwRGQ4MBygLdXoOHtUnifcKnXRFq1oX9P+uKtX2/oTT4SPPoIXX7TgUKuWfRkqV7abboMG4Y2LXxq0bGnzACxfbl+ElBRYvNgCRknbvdtuHs89Z9e4Qwf4/XdLX2qq3eQWL7a0tmkTmzQsXw7t2kFiIuzYkX3Cmg0bLHClpcFZZ9k8Cs6+63Xr2uvgBJUNG+aejyKoQQP7v7n//tB72rWz1/m9x5Ws6tXt/y/qIs2SFPUBDAZeyLJ8KfDfHPt8AHTKsvwp0KGg4xbY0zuLBx+0bPn992evC/jll/wrhcqSzz6zJp3Vq1vP4pL088/Wob5SpVDRxKRJ2ffZt8+uf40a1jdhzZrwjp2cnH8Z7J49Vrn76qvWomTkSNWjj7bzN2xoz5dfbmXxHTqE0tauXfTGBHKurKIiFkklJSXp3LlzY5r2smToUMu2T58OZ5wR23M98YTNXTxunP1qP+ccKybZscOKTvLKpa1aZVn3q66C0aPtFn7bbTBnDgwYYDmRDz6w4oYPP4Q//9kmTbz6avtFe/HF9v7DDrMijRUr7BhZzZxpxSL791sxCcCWLZbzycy0NDZpEttr41xpJxJ5kVRJ5jAqA6uAZoQqvY/LsU8fsld6zy7suOHmMCqKX3+1oSYSE4vWASwczzxjbfqzVow+8ED47fuvucbec/bZoU5wwb4LWStac7b4aNEi+/Lhh1sfiZtvtj4yHTtGZ/hp5yoCSnMrKUsfvYGVWGupfwbWXQ1cHXgtwOjA9sVAUmHH9ICR21tv2V924EAr0pk6teCB3saPt1YwL7yQ/z7r11sb/UWLst+0n3/eioQiaXGUmmody5o2teaczzxjzTBXrrQ0DBtmx+7Tx1rzpKVZe/86dWz/lBQb58kHb3Su6IoSMEqsSCpWvEgqN1W47DJr0XHoodbiBmDuXKsIS0+Hd9+FCRNg40ZrjZWQYC3HFi+21kQzZthk9suXw2efwfz58OWXVsFZs6YVBy1caMVElSpF/zOsW2cVqAkJ0T+2c65oRVIeMMqx77+3JpYbN9rybbdZc7tbboFffrF1derA3/4Gw4ZZgNi9u/DjvvOO1Tc458quogSMGPw2dKVFx47Wlvyjj6wS+NFHrY/Exo3w2GMWUH780fp6NGhgbfSDLrrInuvVgwcesOa7I0dabsODhXMVU0n2w3Bx0KKFPbZts6KoSy6xDnX16uXe99Zbbd/eveHgg60TUc2a1qEprw6EzrmKxYuknHOuAvIiKeecczHjAcM551xYPGA455wLiwcM55xzYfGA4ZxzLiweMJxzzoXFA4ZzzrmweMBwzjkXljLfcU9EdgIr4p2OUuJQYFO8E1FK+LUI8WsR4tcipLWq1orkDeVhaJAVkfZWLK9EZK5fC+PXIsSvRYhfixARiXiIDC+Scs45FxYPGM4558JSHgLG2HgnoBTxaxHi1yLEr0WIX4uQiK9Fma/0ds45VzLKQw7DOedcCfCA4ZxzLixlOmCISC8RWSEiySLy93inpySJyHgR2SAiS7Ksqycin4jIT4HnuvFMY0kQkaNE5HMRWSYiS0XkpsD6ingtqovIbBH5IXAt7gmsr3DXIkhEEkRkgYi8H1iukNdCRFaLyGIRWRhsTluUa1FmA4aIJACjgXOBY4GLROTY+KaqRL0E9Mqx7u/Ap6raEvg0sFzepQO3qGoicCpwXeB7UBGvRSpwlqqeALQHeonIqVTMaxF0E7Asy3JFvhZnqmr7LP1QIr4WZTZgAKcAyaq6SlXTgNeBfnFOU4lR1S+BLTlW9wNeDrx+GehfkmmKB1X9XVXnB17vxG4OR1Ixr4Wq6q7AYpXAQ6mA1wJARBoDfYAXsqyukNciHxFfi7IcMI4E1mZZTgmsq8gaqervYDdSoGGc01OiRKQpcCLwPRX0WgSKYBYCG4BPVLXCXgvgSeA2IDPLuop6LRT4WETmicjwwLqIr0VZHhpE8ljnbYQrKBGpCbwNjFDVHSJ5fT3KP1XNANqLSB3gXRFpG+ckxYWInAdsUNV5ItItzskpDc5Q1XUi0hD4RESWF+UgZTmHkQIclWW5MbAuTmkpLdaLyOEAgecNcU5PiRCRKliwmKCq7wRWV8hrEaSq24AvsHquingtzgD6ishqrLj6LBF5lYp5LVDVdYHnDcC7WJF+xNeiLAeMOUBLEWkmIlWBC4H34pymeHsPuDzw+nJgShzTUiLEshLjgGWq+kSWTRXxWjQI5CwQkRpAD2A5FfBaqOo/VLWxqjbF7g2fqeqfqIDXQkQOFpFawdfAOcASinAtynRPbxHpjZVTJgDjVfWB+Kao5IjIRKAbNlzzeuBfwGTgTaAJ8CswWFVzVoyXKyLSCfgKWEyorPoOrB6jol2LdljlZQL2Y/BNVb1XROpTwa5FVoEiqVtV9byKeC1EpDmWqwCrhnhNVR8oyrUo0wHDOedcySnLRVLOOedKkAcM55xzYfGA4ZxzLiweMJxzzoXFA4ZzzrmweMBwzjkXFg8YrkIQkfqBoZ0XisgfIvJbluWqIjIrRudtLCJD81jfVET2BsZ9Ku45agQ+R5qIHFrc4zmXn7I8lpRzYVPVzdiQ34jISGCXqv47yy6nx+jU3bHh99/IY9vPqtq+uCdQ1b3Y+FGri3ss5wriOQznABHZFfjVv1xEXhCRJSIyQUR6iMg3gUlmTsmy/58CkxUtFJHnAvOz5DxmJ+AJYFBgv2YFnL/QcweGePggMEHSkrxyLs7FkgcM57I7BngKaAe0AS4GOgG3YkOOICKJwFBsBND2QAZwSc4DqerX2Jhn/QIT1/xSzHP3Atap6gmq2haYXqxP6lyEvEjKuex+UdXFACKyFJuRTEVkMdA0sE93oAMwJzCMeg3yH+mzNbAiSudeDPxbRB4B3lfVryL9cM4VhwcM57JLzfI6M8tyJqH/FwFeVtV/FHSgwOBu21V1fzTOraorRaQD0Bt4SEQ+VtV7wzy2c8XmRVLORe5TrF6iIYCI1BORo/PYrxlRnKNFRI4A9qjqq8C/gZOidWznwuE5DOcipKo/isid2JSXlYD9wHXAmhy7LgcOFZElwHBVLW7T3eOBx0QkM3DOa4p5POci4sObOxcHgfnH3w9UXkfrmKuBJFXdFK1jOpeVF0k5Fx8ZwCHR7LgHVCE0iZRzUec5DOecc2HxHIZzzrmweMBwzjkXFg8YzjnnwuIBwznnXFg8YDjnnAuLBwznnHNh8YDhnHMuLB4wnHPOheX/ATNtvjL+wU5vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 0.1\n",
    "mu, sigma = noise_params(0.0, 1.0, dt=dt)\n",
    "print(\"mu = {:.2f}, sigma = {:.2f}\".format(mu, sigma))\n",
    "\n",
    "V, t, ts = simulate(mu, sigma, dt=dt)\n",
    "V_mean_th = V_mean(t, mu)\n",
    "V_std_th = V_std(t, sigma, dt=dt)\n",
    "\n",
    "plt.plot(t, V.mean(axis=1), \"b-\", label=r\"$\\bar{V_m}$\")\n",
    "plt.plot(t + ts, V_mean_th, \"b--\", label=r\"$\\langle V_m \\rangle$\")\n",
    "plt.plot(t, V.std(axis=1), \"r-\", label=r\"$\\sqrt{\\bar{\\Delta V_m^2}}$\")\n",
    "plt.plot(t + ts, V_std_th, \"r--\", label=r\"$\\sqrt{\\langle (\\Delta V_m)^2 \\rangle}$\")\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"Time $t$ [ms]\")\n",
    "plt.ylabel(\"Membrane potential $V_m$ [mV]\")\n",
    "plt.xlim(0, 50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, agreement is fine and the slight drooping artefacts are invisible, since the noise is now updated on every time step. Note also that the noise standard deviation $\\sigma$ is larger (by $\\sqrt{10}$) than for $\\delta=1$ ms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu = 0.00, sigma = 35.36\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:57 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 1002 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 1002\n",
      "    Simulation time (ms): 50\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:57 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 10.0\n",
    "mu, sigma = noise_params(0.0, 1.0, dt=dt)\n",
    "print(\"mu = {:.2f}, sigma = {:.2f}\".format(mu, sigma))\n",
    "\n",
    "V, t, ts = simulate(mu, sigma, dt=dt)\n",
    "V_mean_th = V_mean(t, mu)\n",
    "V_std_th = V_std(t, sigma, dt=dt)\n",
    "\n",
    "plt.plot(t, V.mean(axis=1), \"b-\", label=r\"$\\bar{V_m}$\")\n",
    "plt.plot(t + ts, V_mean_th, \"b--\", label=r\"$\\langle V_m \\rangle$\")\n",
    "plt.plot(t, V.std(axis=1), \"r-\", label=r\"$\\sqrt{\\bar{\\Delta V_m^2}}$\")\n",
    "plt.plot(t + ts, V_std_th, \"r--\", label=r\"$\\sqrt{\\langle (\\Delta V_m)^2 \\rangle}$\")\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"Time $t$ [ms]\")\n",
    "plt.ylabel(\"Membrane potential $V_m$ [mV]\")\n",
    "plt.xlim(0, 50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $\\delta=10$, i.e., a noise switching time equal to $\\tau_m$, the drooping artefact becomes clearly visible. Note that our theory developed above only applies to the points at which the input current switches, i.e., at multiples of $\\delta$, beginning with the arrival of the first current at the neuron (at delay plus one time step). At those points, agreement with theory is good.\n",
    "\n",
    "#### Why does the standard deviation dip between current updates?\n",
    "\n",
    "In the last case, where $\\delta = \\tau_m$, the dips in the membrane potential between changes in the noise current become quite large. They can be explained as follows. For large $\\delta$, we have at the end of a $\\delta$-interval for neuron $n$ membrane potential $V_n(t_{j})\\approx I_{n,j-1}\\tau/C$ and these values will be distributed across neurons with standard deviation $\\sqrt{\\langle (\\Delta V_m)^2 \\rangle}$. Then, input currents of all neurons switch to new values $I_{n,j}$ and the membrane potential of each neuron now evolves towards $V_n(t_{j+1})\\approx I_{n,j}\\tau/C$. Since current values are independent of each other, this means that membrane-potential trajectories criss-cross each other, constricting the variance of the membrane potential before they approach their new steady-state values, as illustrated below.\n",
    "\n",
    "You should therefore use short switching times $\\delta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, V[:, :25], lw=3, alpha=0.5)\n",
    "plt.plot([31.1, 31.1], [-3, 3], \"k--\", lw=2)\n",
    "plt.plot([41.1, 41.1], [-3, 3], \"k--\", lw=2)\n",
    "plt.xlabel(\"Time $t$ [ms]\")\n",
    "plt.ylabel(\"Membrane potential $V_m$ [mV]\")\n",
    "plt.xlim(30, 42)\n",
    "plt.ylim(-2.1, 2.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Autocorrelation\n",
    "\n",
    "We briefly look at the autocorrelation of the membrane potential for three values of $\\delta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import fftconvolve\n",
    "from statsmodels.tsa.stattools import acf\n",
    "\n",
    "\n",
    "def V_autocorr(V_mean, V_std, dt=1.0, tau_m=10.0):\n",
    "    \"Returns autocorrelation of membrane potential and pertaining time axis.\"\n",
    "\n",
    "    mu, sigma = noise_params(V_mean, V_std, dt=dt, tau_m=tau_m)\n",
    "    V, t, ts = simulate(mu, sigma, dt=dt, tau_m=tau_m, t_max=5000.0, N=20)\n",
    "\n",
    "    # drop the first second\n",
    "    V = V[t > 1000.0, :]\n",
    "\n",
    "    # compute autocorrelation columnwise, then average over neurons\n",
    "    nlags = 1000\n",
    "    nt, nn = V.shape\n",
    "    acV = np.zeros((nlags + 1, nn))\n",
    "    for c in range(V.shape[1]):\n",
    "        acV[:, c] = acf(V[:, c], adjusted=True, nlags=1000, fft=True)\n",
    "        # fftconvolve(V[:, c], V[::-1, c], mode='full') / V[:, c].std()**2\n",
    "    acV = acV.mean(axis=1)\n",
    "\n",
    "    # time axis\n",
    "    dt = t[1] - t[0]\n",
    "    acT = np.arange(0, nlags + 1) * dt\n",
    "\n",
    "    return acV, acT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Dec 01 11:25:58 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:58 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 22 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:58 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 22\n",
      "    Simulation time (ms): 5000\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:59 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 22 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 22\n",
      "    Simulation time (ms): 5000\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:25:59 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 22 nodes for simulation.\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 22\n",
      "    Simulation time (ms): 5000\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:25:59 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n"
     ]
    }
   ],
   "source": [
    "acV_01, acT_01 = V_autocorr(0.0, 1.0, 0.1)\n",
    "acV_10, acT_10 = V_autocorr(0.0, 1.0, 1.0)\n",
    "acV_50, acT_50 = V_autocorr(0.0, 1.0, 5.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(acT_01, acV_01, label=r\"$\\delta = 0.1$ms\")\n",
    "plt.plot(acT_10, acV_10, label=r\"$\\delta = 1.0$ms\")\n",
    "plt.plot(acT_50, acV_50, label=r\"$\\delta = 5.0$ms\")\n",
    "\n",
    "plt.xlim(0, 50)\n",
    "plt.ylim(-0.1, 1.05)\n",
    "plt.legend()\n",
    "plt.xlabel(r\"Delay $\\tau$ [ms]\")\n",
    "plt.ylabel(r\"$\\langle V(t)V(t+\\tau)\\rangle$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the autocorrelation is clearly dominated by the membrane time constant of $\\tau_m=10$ ms. The switching time $\\delta$ has a lesser effect, although it is noticeable for $\\delta=5$ ms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Different membrane time constants\n",
    "\n",
    "To document the influence of the membrane time constant, we compute the autocorrelation function for three different $\\tau_m$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Dec 01 11:26:00 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:26:00 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 22 nodes for simulation.\n",
      "\n",
      "Dec 01 11:26:00 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 22\n",
      "    Simulation time (ms): 5000\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:26:00 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n",
      "\n",
      "Dec 01 11:26:00 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:26:00 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 22 nodes for simulation.\n",
      "\n",
      "Dec 01 11:26:00 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 22\n",
      "    Simulation time (ms): 5000\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:26:00 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n",
      "\n",
      "Dec 01 11:26:01 SimulationManager::set_status [Info]: \n",
      "    Temporal resolution changed from 0.1 to 0.1 ms.\n",
      "\n",
      "Dec 01 11:26:01 NodeManager::prepare_nodes [Info]: \n",
      "    Preparing 22 nodes for simulation.\n",
      "\n",
      "Dec 01 11:26:01 SimulationManager::start_updating_ [Info]: \n",
      "    Number of local nodes: 22\n",
      "    Simulation time (ms): 5000\n",
      "    Number of OpenMP threads: 1\n",
      "    Not using MPI\n",
      "\n",
      "Dec 01 11:26:01 SimulationManager::run [Info]: \n",
      "    Simulation finished.\n"
     ]
    }
   ],
   "source": [
    "acV_t01, acT_t01 = V_autocorr(0.0, 1.0, 0.1, 1.0)\n",
    "acV_t05, acT_t05 = V_autocorr(0.0, 1.0, 0.1, 5.0)\n",
    "acV_t10, acT_t10 = V_autocorr(0.0, 1.0, 0.1, 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(acT_t01, acV_t01, label=r\"$\\tau_m = 1$ms\")\n",
    "plt.plot(acT_t05, acV_t05, label=r\"$\\tau_m = 5$ms\")\n",
    "plt.plot(acT_t10, acV_t10, label=r\"$\\tau_m = 10$ms\")\n",
    "\n",
    "plt.xlim(0, 50)\n",
    "plt.ylim(-0.1, 1.05)\n",
    "plt.legend()\n",
    "plt.xlabel(r\"Delay $\\tau$ [ms]\")\n",
    "plt.ylabel(r\"$\\langle V(t)V(t+\\tau)\\rangle$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------------------------\n",
    "#### License\n",
    "\n",
    "This file is part of NEST. Copyright (C) 2004 The NEST Initiative\n",
    "\n",
    "NEST is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.\n",
    "\n",
    "NEST is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
